The offer equates to a value of 100.24p per Evolution share. Evolution fell 1.6 per cent to 92.5p in London trading while Investec fell 3 per cent to 414.6p.
"The deal builds incremental funds under management in the area which we believe is most under-appreciated and hence most undervalued at Investec," said Numis Securities analysts.
"We expect this to change in time as the market gives more valuation benefit to what is now a large asset management business."
Numis is keeping its "buy" recommendation on Investec.
Evolution chief executive Alex Snow will become the executive chairman of Investec's UK investment banking division, while David Currie will continue as head of Investec's British investment banking unit.
Investec also said it aimed to shed staff at the investment banking unit to "avoid unnecessary overlap with its existing activities".
The Investec offer is conditional on regulatory conditions and a document will be posted to Evolution shareholders followed by a general meeting in November.
- BLOOMBERG